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From: olcott <polcott333@gmail.com>
Newsgroups: comp.theory
Subject: Re: How to write a self-referencial TM?
Date: Sun, 18 May 2025 17:09:47 -0500
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On 5/18/2025 4:46 PM, wij wrote:
> On Sun, 2025-05-18 at 15:57 -0500, olcott wrote:
>> On 5/18/2025 3:35 PM, wij wrote:
>>> On Sat, 2025-05-17 at 14:39 -0500, olcott wrote:
>>>> On 5/17/2025 2:26 PM, wij wrote:
>>>>> On Sat, 2025-05-17 at 15:45 +0100, Mike Terry wrote:
>>>>>> On 17/05/2025 04:01, wij wrote:
>>>>>>> On Fri, 2025-05-16 at 23:51 +0100, Mike Terry wrote:
>>>>>>>> On 16/05/2025 20:35, wij wrote:
>>>>>>>>> On Fri, 2025-05-16 at 16:33 +0100, Mike Terry wrote:
>>>>>>>>>> On 16/05/2025 12:40, wij wrote:
>>>>>>>>>>> On Fri, 2025-05-16 at 03:26 +0100, Mike Terry wrote:
>>>>>>>>>>>> On 16/05/2025 02:47, wij wrote:
>>>>>>>>>>>>> On Fri, 2025-05-16 at 01:40 +0100, Mike Terry wrote:
>>>>>>>>>>>>>> On 15/05/2025 19:49, wij wrote:
>>>>>>>>>>>>>>> On Thu, 2025-05-15 at 17:08 +0100, Mike Terry wrote:
>>>>>>>>>>>>>>>> On 14/05/2025 18:53, wij wrote:
>>>>>>>>>>>>>>>>> On Wed, 2025-05-14 at 12:24 -0500, olcott wrote:
>>>>>>>>>>>>>>>>>> On 5/14/2025 11:43 AM, wij wrote:
>>>>>>>>>>>>>>>>>>> On Wed, 2025-05-14 at 09:51 -0500, olcott wrote:
>>>>>>>>>>>>>>>>>>>> On 5/14/2025 12:13 AM, wij wrote:
>>>>>>>>>>>>>>>>>>>>> Q: Write a turing machine that performs D function (which
>>>>>>>>>>>>>>>>>>>>> calls
>>>>>>>>>>>>>>>>>>>>> itself):
>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>> void D() {
>>>>>>>>>>>>>>>>>>>>>             D();
>>>>>>>>>>>>>>>>>>>>> }
>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>> Easy?
>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>> That is not a TM.
>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>> It is a C program that exists. Therefore, there must be a
>>>>>>>>>>>>>>>>>>> equivalent
>>>>>>>>>>>>>>>>>>> TM.
>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>> To make a TM that references itself the closest
>>>>>>>>>>>>>>>>>>>> thing is a UTM that simulates its own TM source-code.
>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>> How does a UTM simulate its own TM source-code?
>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>> You run a UTM that has its own source-code on its tape.
>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>> What is exactly the source-code on its tape?
>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>> Every UTM has some scheme which can be applied to a (TM & input tape)
>>>>>>>>>>>>>>>> that
>>>>>>>>>>>>>>>> is to
>>>>>>>>>>>>>>>> be
>>>>>>>>>>>>>>>> simulated.
>>>>>>>>>>>>>>>> The
>>>>>>>>>>>>>>>> scheme says how to turn the (TM + input tape) into a string of symbols
>>>>>>>>>>>>>>>> that
>>>>>>>>>>>>>>>> represent
>>>>>>>>>>>>>>>> that
>>>>>>>>>>>>>>>> computation.
>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>> So to answer your question, the "source-code on its tape" is the result
>>>>>>>>>>>>>>>> of
>>>>>>>>>>>>>>>> applying
>>>>>>>>>>>>>>>> the
>>>>>>>>>>>>>>>> UTM's
>>>>>>>>>>>>>>>> particular scheme to the combination (UTM, input tape) that is to be
>>>>>>>>>>>>>>>> simulated.
>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>> If you're looking for the exact string symbols, obviously you would need
>>>>>>>>>>>>>>>> to
>>>>>>>>>>>>>>>> specify
>>>>>>>>>>>>>>>> the
>>>>>>>>>>>>>>>> exact
>>>>>>>>>>>>>>>> UTM
>>>>>>>>>>>>>>>> being used, because every UTM will have a different answer to your
>>>>>>>>>>>>>>>> question.
>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>> Mike.
>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>> People used to say UTM can simulate all TM. I was questing such a UTM.
>>>>>>>>>>>>>>> Because you said "Every UTM ...", so what is the source of such UTM?
>>>>>>>>>>>>>>
>>>>>>>>>>>>>> Yes, a UTM can simulate any TM including itself.  (Nothing magical changes
>>>>>>>>>>>>>> when
>>>>>>>>>>>>>> a
>>>>>>>>>>>>>> UTM
>>>>>>>>>>>>>> simulates
>>>>>>>>>>>>>> itself, as opposed to some other TM.)
>>>>>>>>>>>>>
>>>>>>>>>>>>> Supposed UTM exists, and denoted as U(X), X denotes the tape contents of the
>>>>>>>>>>>>> encoding of a TM. And, U(X) should function the same like X.
>>>>>>>>>>>>> Given instance U(U(f)), it should function like f from the above definition.
>>>>>>>>>>>>> But, U(U(f)) would fall into a 'self-reference' trap.
>>>>>>>>>>>>
>>>>>>>>>>>> There is no self-reference trap.
>>>>>>>>>>>>
>>>>>>>>>>>> In your notation:
>>>>>>>>>>>>
>>>>>>>>>>>> -  f represents some computation.
>>>>>>>>>>>> -  U(f) represents U being run with f on its tape.
>>>>>>>>>>>>           Note this is itself a computation, distinct from f of course
>>>>>>>>>>>>           but having the same behaviour.
>>>>>>>>>>>> -  U(U(f)) represents U simulating the previous computation.
>>>>>>>>>>>>
>>>>>>>>>>>> There is no reason U(f) cannot be simulated by U.  U will have no knowledge that
>>>>>>>>>>>> it
>>>>>>>>>>>> is
>>>>>>>>>>>> "simulating
>>>>>>>>>>>> itself", and will just simulate what it is given.
>>>>>>>>>>>>
>>>>>>>>>>>>
>>>>>>>>>>>> Mike.
>>>>>>>>>>>
>>>>>>>>>>> Sorry for not being clear on the UTM issue (I wanted to mean several things in one
>>>>>>>>>>> post).
>>>>>>>>>>> You are right there is no self-reference.
>>>>>>>>>>> I mean 'UTM' is not a complete, qualified TM because the contents of the tape
>>>>>>>>>>> would not be defined. Saying "UTM can simulate any TM" is misleading because
>>>>>>>>>>> no such TM (UTM as TM) exists.
>>>>>>>>>>
>>>>>>>>>> What do you mean "the contents of the tape would not be defined"?  A TM is
>>>>>>>>>> /equipped/
>>>>>>>>>> with
>>>>>>>>>> an
>>>>>>>>>> infinite tape, but the /contents/ of that tape are not a part of that TM's
>>>>>>>>>> definition.
>>>>>>>>>>
>>>>>>>>>> For example we could build a TM P that decides whether a number is prime.  Given a
>>>>>>>>>> number n,
>>>>>>>>>> we
>>>>>>>>>> convert n into the input tape representation of n, and run P with that tape as
>>>>>>>>>> input.
>>>>>>>>>>
>>>>>>>>>> It's essentially no different for UTMs.  Such a UTM certainly is a "complete TM",
>>>>>>>>>> equipped
>>>>>>>>>> with
>>>>>>>>>> its
>>>>>>>>>> own input tape.  Of course we don't know what's on the input tape because nobody has
>>>>>>>>>> said
>>>>>>>>>> yet
>>>>>>>>>> what
>>>>>>>>>> computation we are asking it to simulate!  [Similarly we don't know what's on P's
>>>>>>>>>> input
>>>>>>>>>> tape,
>>>>>>>>>> until
>>>>>>>>>> we know what n we want it to test for primeness.]  Once you say what computation you
>>>>>>>>>> want
>>>>>>>>>> the
>>>>>>>>>> UTM to
>>>>>>>>>> simulate we can build a tape string to perform that particular simulation.  That is
>>>>>>>>>> the
>>>>>>>>>> case
>>>>>>>>>> /whatever/ computation we come up with, so it is simply the case [not misleading]
>>>>>>>>>> that
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